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Runtime Complexity: TRS pair #487111534
details
property
value
status
complete
benchmark
2.23.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n140.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.526 seconds
cpu usage
953.042
user time
946.692
system time
6.35038
max virtual memory
5.6905864E7
max residence set size
8040396.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^3), ?)
output
WORST_CASE(Omega(n^3), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) typed CpxTrs (5) OrderProof [LOWER BOUND(ID), 0 ms] (6) typed CpxTrs (7) RewriteLemmaProof [LOWER BOUND(ID), 278 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 38 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^2, INF) (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 654 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 5927 ms] (22) proven lower bound (23) LowerBoundPropagationProof [FINISHED, 0 ms] (24) BOUNDS(n^3, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, INF). The TRS R consists of the following rules: fac(0) -> 1 fac(s(x)) -> *(s(x), fac(x)) floop(0, y) -> y floop(s(x), y) -> floop(x, *(s(x), y)) *(x, 0) -> 0 *(x, s(y)) -> +(*(x, y), x) +(x, 0) -> x +(x, s(y)) -> s(+(x, y)) 1 -> s(0) fac(0) -> s(0) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^3, INF). The TRS R consists of the following rules: fac(0') -> 1' fac(s(x)) -> *'(s(x), fac(x)) floop(0', y) -> y floop(s(x), y) -> floop(x, *'(s(x), y)) *'(x, 0') -> 0' *'(x, s(y)) -> +'(*'(x, y), x) +'(x, 0') -> x +'(x, s(y)) -> s(+'(x, y)) 1' -> s(0') fac(0') -> s(0') S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: TRS: Rules: fac(0') -> 1' fac(s(x)) -> *'(s(x), fac(x)) floop(0', y) -> y floop(s(x), y) -> floop(x, *'(s(x), y)) *'(x, 0') -> 0' *'(x, s(y)) -> +'(*'(x, y), x) +'(x, 0') -> x +'(x, s(y)) -> s(+'(x, y))
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